How do you solve $x^2-2x-24=0$ using the quadratic formula?

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How do you solve $x^2-2x-24=0$ using the quadratic formula?

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Answer 1 · 2016-02-29T10:38:10

$x = 6, -4$

Explanation:

The quadratic formula is:

$x = (-b +- sqrt(b^2 - 4ac))/(2a)$

and the general formula of a quadratic equation is:

$ax^2 + bx + c = 0$

With our current example, $x^2 - 2x - 24 = 0$ , we know that our is already in the standard form hence we do not need to do any manipulations to compute for $x$ .

[Solution]

$x^2 - 2x - 24 = 0$

We know that:
$a = 1$
$b = -2$
$c = -24$

Evaluating the quadratic equation with the values above...

$x = (-b +- sqrt(b^2 - 4ac))/(2a)$
$x = (-(-2) +- sqrt((-2)^2 - 4(1)(-24)))/(2(1))$
$x = (2 +- sqrt(4 + 96))/2$
$x = (2 +- sqrt(100))/2$
$x = (2 +- 10)/2$
$x = 12/2 , -8/2$
$x = 6, -4$

[Checking -> Using Factorisation]
$x^2 - 2x - 24 = 0$
$(x - 6)(x + 4) = 0$
$x = 6, -4$

Since we got the same answer for both method, we know that our answer is correct.

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How do you solve $x^2-2x-24=0$ using the quadratic formula?

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How do you solve $x^2-2x-24=0$ using the quadratic formula?